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Q: 1. Evaluate the following limits. L'Hopital's rule is NOT allowed. 2-√√x-1 1. lim x-5 x² - 4x - 5 2x…

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Q: I. Evaluate the following limits. Using L'Hôpital's Rule is not allow 1+ 3/ 1. lim. 1 2x²+x-1

A: Given: limx→ -11+1x32x2+x-1

Q: Solve the given initial value problem and determine at least approximately where the solution is…

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Q: Find Do not simplify your answers. dy da 1. log;(√2x² + y) + tan(x² − 7") = sin¯'¹(x² − 1) + ½

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Q: /² sin ( cos() sin() dx (Consider initially the first 2 terms)

A: To evaluate the value of given integral.

Q: Given : A B Ⓒ E b 27π²-24 [x³sin(2x) dx = . 64 2π 3 3π 4 TU 4 =|m 5 T 6 Find b if Isb -SOST

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Q: The junior class has 50 students. Twenty-five students take French, 15 take Latin, and 10 take both.…

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Q: 5. f(x)= x³; [2, 3]

A: To calculate area under curve we have to integrate the function within the given limits Please note:…

Q: b √x³sin(2x) dx = 2π 3 플 FIM 27π²-24 64 Find bif sb

A: Solution of the problem as follows

Q: 1o. 1 |x-3|dx

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Q: (D² – D − 2)y = cos x

A: Here is the solution:

Q: I. Evaluate the following limits. Using L'Hôpital's Rule is not allowed. 3. lim (x-3) tan(9-x²)…

A: Formulas of limits which have been used are written in the solution

Q: mposition =

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Q: Definite Integral and Plane Areas by integration (snow solution) dx + So - 2 1+x 2. S dx 25-x2 = 1/2…

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Q: Solve the initial value problem y' = 4 cos(4x) 3+ 2y , y(0) = -1 and determine where the solution…

A: Given IVP y'=4cos (4x)3+2y , y(0)=-1

Q: Use the formula ‹(t) = = 198 t7 k(t) : (4+121 +¹8) ²³/ = ||r' (t) x r"(t)|| r(t) = t²i+t¹¹j X to…

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Q: A 48 B 96 0 D 32 If f cos42t dt = At - B sin 2t cos 2t + D sin 4t cos 4t + C where A, B, C and D are…

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Q: The IBP formula fudv-uv- - fvdu can also be written as fudv + ſ vdu = uv Which of the following…

A: Given that the four options  To find choose the correct option which is satisfi IBP formula

Q: A B C The IBP formula fudv=uv-fvdu can also be written as f udv + ſ vdu : = UV Which of the…

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Q: y"+6y' +8y=10e-³x ;

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Q: * Evaluate. [12 [20x cos(5x² - 1)]dx

A: The given integral is   ∫20xcos5x2-1 dx We solve the integral using proper substitution .

Q: Select the conic section represented by the equation. x 2 +y 2 + 6x - 4y - 12 = 0. circle point…

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Q: 1. Evaluate the following limits. L'Hopital's rule is NOT allowed. 2-√x-1 1. lim 4. lim 5 3x - 4 2.…

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Q: Find a set of parametric equations of the line through the point (1,-2, 3) and perpendicular to the…

A: Given point(1,-2,3) Then the equation of the line passing through 1,-2,3 is…

Q: Find all Max., Min., Saddle point for the functions below: P(x) = 2xy-5x²-29² + 4x +49-4

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Q: At each point (x,y) on the curve, the slope is 2x+1. The curve passes through the point (-3,0). Find…

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Q: ST/4 x² dx (x²+4)5/2 (Use trigonometric substitution)

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Q: I. Evaluate the following limits. Using L'Hôpital's Rule is not allowed. 1 + ²/ 1. lim x12x² + x1

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Q: 17 Select the conic section represented by the equation. 4x 2 -y 2 + 24x + 4y + 28 = 0. circle…

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Q: 31. (a) |2x - 1| dx (b) 3π/4 1.T CT/2 \cos x dx

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Q: x²+x+1 rb dx g(x) Sa 2x²+2+73+x dx =[Af (x) - B ln(g(x)] + D fod, and if A =,B<0, then dx = P x+2'…

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Q: 31. (a) 32. (a) 33. (a) 12x-1| dx √2 + x) dx e* - 1| dx L'i lex -3π/4 (b) cos x dx (b) [*/² | } −…

A: Given: ∫-11ex-1dx

Q: if any. Find the absolute extremum point(s) of f(x) = el-cost on [−5, π],

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Q: 2 Find the center of the following equation.      x 2 +y 2 + 8x - 6y - 15 = 0 (4, 3) (8, -6) (-4,…

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Q: A) 48 B) 0 96 D) 32 If f cos42t dt = At - B sin 2t cos 2t + D sin 4t cos 4t + C where A, B, C and D…

A: To value of the value of given integration in terms of given values .

Q: 8 An acceleration function is expressed as a (s, v) = s²-. ' (v+1)³ determine displacement by…

A: a(s, v)=s2-8(v+1)3v(s)=∫0s a(s, v) dv      =∫0s s2-8(v+1)3 dv     =s2v0s -8 (v+1)-3+1-3+10s     =s2s…

Q: Find parametric equations of the line that satisfies the stated conditions. The line through (-3, 0,…

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Q: dy II. Find Do not simplify your answers. . dx 2. y= tan-¹(cosh.r) (sin²r) (sech r)secr [use…

A: Given y=tan-1( cosh x)( sin2 x ) (sech x)secx

Q: The radius of a circle increases at a rate of 2 m/s. Find the rate at which the area of the circle…

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Q: 62. du * |x|dx

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Q: dx secx+1

A: First simply the equation Using Trigonometric identities.

Q: Find the directional derivative of f(x, y) = direction of Q(2, —2). NOTE: Enter the exact answer.…

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Q: Find Duf at P. NOTE: Enter the exact answer. Duf = f(x, y) = sin(3x – 4y); P(4,3); u || 35 i I

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Q: Find the curvature K of the curve, where s is the arc length parameter. M(²) = (₁ + √2/2 =) ₁ - (₁ -…

A: we have to find curvature.

Q: 1. xý + 3y += sin x v2

A: Given :

Q: e²+2y + sech T = cot y + log2 (tanh x)

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Let a = ci + j and b = 6i + 36j. Find c so that a and b are orthogonal. C = i

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Q: 4 Identify the center of the conic section whose equation is x 2 +y 2 + 6x - 4y - 12 = 0. (-6, 4)…

A: The given equation is; x2+y2+6x-4y-12=0   As we know that; The general form of equation of the…

Q: Find the degree of the term 126: Find the degree of the term - 6: Find the degree of the term - 12³:…

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Q: ... : S (1 + 2x) e-x dx. Using integration by parts and letting u = -1- 2x, dv = 2 f(x)dx, then the…

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